Vlasov simulations of very-large-amplitude-wave generation in the plasma wake-field accelerator

Simulations of the plasma wake-field accelerator are carried out by following the time evolution of the plasma distribution function in one dimension via the Vlasov-Maxwell equations. Simulation results are compared to numerical solutions of the nonlinear relativistic cold plasma equations and to previous theoretical estimations of trapping and thermal effects on plasma waves. It is found that highly nonlinear wakes are obtainable in the vicinity of the driving beam; where the thermal velocity spread of the plasma is reduced. In this region; wake amplitudes can significantly exceed the expectations of relativistic warm plasma models and agree closely with cold fluid theory. In all cases; however; particle trapping and thermalization due to particle scattering from the large-amplitude plasma wave reduce the wake to below the nonrelativistic wave-breaking limit after the initial accelerating peak.